Method for locally refining a mesh

Abstract

A method, i.e. the so-called Cube-Assembling Method (CAM), is disclosed for locally refining a n-dimensional mesh in a predetermined domain, wherein the mesh comprises nodes and n−1 planes connecting these nodes thereby dividing said domain in n-dimensional first elements. By applying a mesh on a domain, the domain can be introduced in a computer aided design environment for optimization purposes. Concerning the mesh, one of the issues is to perform the optimization using the appropriate amount of nodes at the appropriate location The method of the present invention succeeds in adding or removing nodes locally. The assembling is done over the elements, being e.g. squares or cubes or hypercubes dependent of the dimension of the mesh. Like the finite-box method, the CAM method is easy to program, even in higher dimensions. However, the CAM method does not suffer from the restriction that only one line may terminate at the side of a box.

What is claimed is:  
     
       1. A method of modeling at least one characteristic of a device, the method comprising: 
       generating, in a computer, a n-dimensional mesh in a predetermined domain, wherein the mesh comprises nodes and n−1 planes connecting these nodes thereby dividing the domain in n-dimensional first elements wherein each element is defined by 2 n  nodes, and wherein the n-dimensional mesh models the at least one characteristic of the device;  
       creating a first additional node inside at least one of said first elements by completely splitting said first element in exactly 2 n  nodes n-dimensional second elements in such a manner that said first additional node forms a corner node of each of said second elements which results in the replacement of said first element by said 2 n  n-dimensional second elements;  
       creating a second additional node inside at least one of said second elements by completely splitting said first element in exactly 2 n  nodes n-dimensional third elements in such a manner that said second additional node forms a corner node of each of said third elements which results in the replacement of said first element by said 2 n  n-dimensional third elements;  
       providing at least one equation for each node of the n-dimensional mesh; and  
       solving together each of the provided equations.  
     
     
       2. The method of  claim 1 , wherein after locally refining said n-dimensional mesh, said n-dimensional mesh is locally coarsened. 
     
     
       3. The method of  claim 1 , wherein said refinement is based on an adaptive meshing strategy. 
     
     
       4. The method of  claim 1 , wherein the device comprises an electronic circuit device. 
     
     
       5. The method of  claim 1 , wherein the device comprises an electronic circuit that is part of a semiconductor integrated circuit. 
     
     
       6. The method of  claim 1 , wherein the characteristic is an electrical potential of a device. 
     
     
       7. The method of  claim 1 , wherein each of the provided equations comprises a node balance that is indicative of at least two link currents across a link to each of the respective nodes. 
     
     
       8. A program storage device, storing instructions that when executed by a computer perform the method comprising: 
       generating, in a computer, a n-dimensional mesh in a predetermined domain, wherein the mesh comprises nodes and n−1 planes connecting these nodes thereby dividing the domain in n-dimensional first elements wherein each element is defined by 2 n  nodes, and wherein the n-dimensional mesh models the at least one characteristic of a device;  
       creating a first additional node inside at least one of said first elements by completely splitting said first element in exactly 2 n  n-dimensional second elements in such a manner that said first additional node forms a corner node of each of said second elements which results in the replacement of said first element by said 2 n  n-dimensional second elements;  
       creating a second additional node inside at least one of said second elements by completely splitting said second element in exactly 2 n  n-dimensional third elements in such a manner that said second additional node forms a corner node of each of said third elements which results in the replacement of said second element by said 2 n  n-dimensional third elements;  
       providing at least one equation for each node of the n-dimensional mesh; and  
       solving together each of the provided equations.  
     
     
       9. The program storage device of  claim 8 , wherein the device comprises an electronic circuit device. 
     
     
       10. The program storage device of  claim 8 , wherein the device comprises an electronic circuit that is part of a semiconductor integrated circuit. 
     
     
       11. The program storage device of  claim 8 , wherein the characteristic is an electrical potential of a device. 
     
     
       12. The program storage device of  claim 8 , wherein each of the provided equations comprises a node balance that is indicative of at least two link currents across a link to each of the respective nodes. 
     
     
       13. A method of modeling at least one characteristic of a device, the method comprising: 
       generating, in a computer, a n-dimensional mesh in a predetermined domain, wherein the mesh comprises nodes and n−1 planes connecting these nodes thereby dividing the domain in n-dimensional first elements wherein each element is defined by 2 n  nodes, and wherein the n-dimensional mesh models the at least one characteristic of the device;  
       creating a first additional node inside at least one of said first elements by completely splitting said first element in exactly 2 n  nodes n-dimensional second elements in such a manner that said first additional node forms a corner node of each of said second elements which results in the replacement of said first element by said 2 n  n-dimensional second elements;  
       creating a second additional node inside at least one of said second elements by completely splitting said first element in exactly 2 n  nodes n-dimensional third elements in such a manner that said second additional node forms a corner node of each of said third elements which results in the replacement of said first element by said 2 n  n-dimensional third elements;  
       providing at least one equation for each node of the n-dimensional mesh;  
       solving together each of the provided equations, wherein the solved equations provides modeling information that is indicative of the characteristic of the device; and  
       displaying said modeled information.  
     
     
       14. The method of  claim 13 , wherein the device comprises an electronic circuit device. 
     
     
       15. The method of  claim 13 , wherein the device comprises an electronic circuit that is part of a semiconductor integrated circuit. 
     
     
       16. The method of  claim 13 , wherein the characteristic is an electrical potential of a device. 
     
     
       17. The method of  claim 13 , wherein each of the provided equations comprises a node balance that is indicative of at least two link currents across a link to each of the respective nodes.